1. Total variable costs change in proportion to changes in the level of activity. Unit variable
costs remain the same regardless of the level of activity.
2. a. Variable costs
b. Variable costs
3. Total fixed cost remains the same regardless of changes in the level of activity. Fixed cost per unit
decreases as the activity level increases and increases as the activity level decreases.
4. Mixed costs are costs that have characteristics of both a variable and a fixed cost. The high-low
method uses the highest and lowest activity levels and their related costs to estimate the variable cost per unit and the fixed cost. The total fixed cost does not change with changes in activity level. Thus, the difference in the total cost between the highest and lowest levels of activity is the change in the total variable cost. Dividing this difference by the difference in activity level is an estimate of the variable cost per unit. The fixed cost is then estimated by subtracting the total variable costs from the total costs for the level of activity.
5. a. No impact on the contribution margin.
b. Income from operations would decrease.
6. A high contribution margin ratio, coupled with idle capacity, indicates a potential for increased
income from operations if additional sales can be made. A large percentage of each additional sales dollar would be available, after providing for variable costs, to cover promotion efforts and to increase income from operations. Thus, a substantial sales promotion campaign should be considered in order to expand sales to maximum capacity and to take advantage of the low ratio of variable costs to sales.
7. Decreases in unit variable costs, such as a decrease in the unit cost of direct materials, will
decrease the break-even point.
8. Austin Company had lower fixed costs and a higher percentage of variable costs to sales than
did Hill Company. Such a situation resulted in a lower break-even point for Austin Company.
9. The individual products are treated as components of one overall enterprise product. These
components are weighted by the sales mix percentages when determining the contribution margin. Therefore, the sales mix affects the contribution margin and thus the break-even point.
PE 19–1A (FIN MAN); PE 4–1A (MAN)
a. $23 per unit = ($700,000 – $240,000) ÷ (30,000 units – 10,000 units)
b. $10,000 = $700,000 – ($23 × 30,000 units), or $240,000 – ($23 × 10,000 units)
PE 19–1B (FIN MAN); PE 4–1B (MAN)
a. $50 per unit = ($440,000 – $300,000) ÷ (5,500 units – 2,700 units)
b. $165,000 = $440,000 – ($50 × 5,500 units), or $300,000 – ($50 × 2,700 units)
PE 19–2A (FIN MAN); PE 4–2A (MAN)
a. 37.5% = ($80 – $50) ÷ $80, or ($480,000 – $300,000) ÷ $480,000 b. $30 per unit = $80 – $50
c. Sales……… $480,000 (6,000 units × $80 per unit) Variable costs……… 300,000 (6,000 units × $50 per unit) Contribution margin……… $180,000 (6,000 units × $30 per unit) Fixed costs……… 50,000
Income from operations……… $130,000
PE 19–2B (FIN MAN); PE 4–2B (MAN)
a. 20% = ($30 – $24) ÷ $30, or ($660,000 – $528,000) ÷ $660,000 b. $6 per unit = $30 – $24
c. Sales……… $660,000 (22,000 units × $30 per unit) Variable costs……… 528,000 (22,000 units × $24 per unit) Contribution margin……… $132,000 (22,000 units × $6 per unit) Fixed costs……… 40,000
a. 1,500 units = $45,000 ÷ ($90 – $60) b. 900 units = $45,000 ÷ ($110 – $60)
PE 19–3B (FIN MAN); PE 4–3B (MAN) a. 1,600 units = $48,000 ÷ ($75 – $45) b. 960 units = $48,000 ÷ ($95 – $45)
PE 19–4A (FIN MAN); PE 4–4A (MAN) a. 1,000 units = $25,000 ÷ ($80 – $55)
b. 1,800 units = ($25,000 + $20,000) ÷ ($80 – $55)
PE 19–4B (FIN MAN); PE 4–4B (MAN) a. 5,000 units = $200,000 ÷ ($150 – $110)
b. 6,250 units = ($200,000 + $50,000) ÷ ($150 – $110)
PE 19–5A (FIN MAN); PE 4–5A (MAN)
Unit selling price of E: [($150 × 0.70) + ($100 × 0.30)] = $135.00 Unit variable cost of E: [($100 × 0.70) + ($75 × 0.30)] = 92.50
Unit contribution margin of E: $ 42.50
Break-Even Sales (units) = 12,000 units = $510,000 ÷ $42.50
Break-Even Sales (units) for AA = 12,000 units of E × 70% = 8,400 units of Product AA Break-Even Sales (units) for BB = 12,000 units of E × 30% = 3,600 units of Product BB
PE 19–5B (FIN MAN); PE 4–5B (MAN)
Unit selling price of E: [($50 × 0.40) + ($60 × 0.60)] = $56.00 Unit variable cost of E: [($35 × 0.40) + ($30 × 0.60)] = 32.00
Contribution Margin $160,000 Income from Operations $80,000
PE 19–6B (FIN MAN); PE 4–6B (MAN)
Contribution Margin $450,000 Income from Operations $300,000
PE 19–7A (FIN MAN); PE 4–7A (MAN)
= ($1,200,000 – $960,000) ÷ $1,200,000 = 20%
PE 19–7B (FIN MAN); PE 4–7B (MAN)
Margin of Safety = ($550,000 – $385,000) ÷ $550,000 = 30% Margin of Safety = Sales –Sales at Break-Even Point
Sales Operating Leverage
Operating Leverage
Margin of Safety Margin of Safety
= Sales –Sales at Break-Even Point Sales
= 2
= = = 1.5
Ex. 19–1 (FIN MAN); Ex. 4–1 (MAN) 1. Fixed 9. Fixed 2. Fixed 10. Variable 3. Variable 11. Variable 4. Variable 12. Mixed 5. Fixed 13. Variable 6. Variable 14. Variable 7. Variable 15. Mixed 8. Variable
Ex. 19–2 (FIN MAN); Ex. 4–2 (MAN)
a. Cost Graph Three d. Cost Graph Two
b. Cost Graph Four e. Cost Graph Two
c. Cost Graph One
Ex. 19–3 (FIN MAN); Ex. 4–3 (MAN)
1. e 4. f
2. b 5. d
3. c 6. a
Ex. 19–4 (FIN MAN); Ex. 4–4 (MAN) 1. e
2. f 3. c
For 3. (c) is better than (b) because the administrative costs would be the same for expensive and inexpensive cars.
a. Fixed g. Variable b. Fixed h. Variable c. Variable i. Fixed d. Fixed j. Variable e. Fixed* k. Variable f. Variable
*The developer salaries are fixed because they are more variable to the number of titles or releases, rather than the number of units sold. For example, a title could sell one copy or a million copies, and the salaries of the developers would not be affected.
Ex. 19–6 (FIN MAN); Ex. 4–6 (MAN)
Components produced………… 400,000 480,000 600,000
Total costs:
Total variable costs………… $160,000 (d) $192,000 (j) $240,000 Total fixed costs……… 240,000 (e) 240,000 (k) 240,000 Total costs……… $400,000 (f) $432,000 (l) $480,000 Cost per unit:
Variable cost per unit…………(a) $ 0.40 (g) $ 0.40 (m) $ 0.40 Fixed cost per unit………(b) 0.60 (h) 0.50 (n) 0.40 Total cost per unit………(c) $ 1.00 (i) $ 0.90 (o) $ 0.80 Supporting calculations:
a. $0.40 ($160,000 ÷ 400,000 units) b. $0.60 ($240,000 ÷ 400,000 units) d. $192,000 ($0.40 × 480,000)
e. $240,000 (fixed costs do not change with volume)
g. $0.40 ($192,000 ÷ 480,000 units; variable costs per unit do not change with changes in volume)
h. $0.50 ($240,000 ÷ 480,000 units) j. $240,000 ($0.40 × 600,000 units)
k. $240,000 (fixed costs do not change with volume)
m. $0.40 ($240,000 ÷ 600,000 units; variable costs per unit do not change with changes in volume)
$165,000 10,000 units
The fixed cost can be determined by subtracting the estimated total variable cost from the total cost at either the highest or lowest level of production, as follows:
Total Cost = (Variable Cost per Unit × Units Produced) + Fixed Costs Highest level:
$690,000 = ($16.50 × 18,100 units) + Fixed Costs $690,000 = $298,650 + Fixed Costs
$391,350 = Fixed Costs Lowest level:
$525,000 = ($16.50 × 8,100 units) + Fixed Costs $525,000 = $133,650 + Fixed Costs
$391,350 = Fixed Costs
b. Total Cost = (Variable Cost per Unit × Units Produced) + Fixed Costs Total cost for 12,000 units:
Variable cost:
Units……… 12,000 Variable cost per unit……… $16.50
Total variable cost……… $198,000
Fixed costs……… 391,350
Total cost……… $589,350
= Variable Cost per Unit =
= Variable Cost per Unit a.
$16.50 per unit Variable Cost per Unit =
Difference in Total Costs Difference in Units Produced
$690,000 – $525,000 18,100 units – 8,100 units
The fixed costs can be determined by subtracting the estimated total variable cost from the total cost at either the highest or lowest level of gross-ton mile, as follows:
Total Cost = (Variable Cost per Gross-Ton Mile × Gross-Ton Miles) + Fixed Costs Highest level:
$1,750,000 = ($1.80 × 750,000 gross-ton miles) + Fixed Costs $1,750,000 = $1,350,000 + Fixed Costs
$400,000 = Fixed Costs Lowest level:
$1,255,000 = ($1.80 × 475,000 gross-ton miles) + Fixed Costs $1,255,000 = $855,000 + Fixed Costs
$400,000 = Fixed Costs
Ex. 19–9 (FIN MAN); Ex. 4–9 (MAN) a. Sales………$2,750,000 Variable costs……… 1,760,000 Contribution margin………$ 990,000 $990,000 $2,750,000 b. Sales………
Contribution margin ratio……… Contribution margin……… Less fixed costs……… Income from operations………
Variable Cost per Gross-Ton Mile =
= Variable Cost per
Gross-Ton Mile Difference in Gross-Ton Miles Difference in Total Costs
750,000 gross-ton miles – 475,000 gross-ton miles $1,750,000 – $1,255,000
275,000 gross-ton miles
Contribution Margin Ratio =
Sales – Variable Costs Sales
Variable Cost per
Gross-Ton Mile = =
$495,000
$1.80 per gross-ton miles
$ 224,000 356,000 Contribution Margin Ratio = = 36% $1,450,000 40% $ 580,000 ×
a. Sales (in millions)……… $16,233 Variable costs (in millions):
Food and packaging……… $ 5,300
Payroll……… 4,121
General, selling, and administrative expenses (40% × $2,334)………… 934 Total variable costs……… $10,355 Contribution margin (in millions)……… $ 5,878
$5,878 million $16,233 million
c. Same-store sales increase (in millions)……… Contribution margin ratio (in millions) [from part (b)]……… Increase in income from operations (in millions)………
Note to Instructors: Part (c) emphasizes “same-store sales” because of the assumption of no change in fixed costs. McDonald’s will also increase sales from opening new stores. However, the impact on income from operations for these additional store sales would need to include an increase in fixed costs into the calculation.
Ex. 19–11 (FIN MAN); Ex. 4–11 (MAN)
$900,000 $120 – $75
b. Sales (units) = Fixed Costs + Target Profit Unit Contribution Margin a. Break-Even Sales (units) = Fixed Costs
Unit Contribution Margin Break-Even Sales (units) = = 20,000 units
$294 million $811 million
36.2% Contribution Margin Ratio = = 36.2%
Sales – Variable Costs Sales
b. Contribution Margin Ratio =
Total Cost Variable Cost Variable Cost (in millions) Percentage (in millions)
Cost of goods sold……… $16,151.0 × 70% = $11,305.7
Selling, general and administrative……… 9,249.0 × 40% = 3,699.6
Total Cost Variable Cost Fixed Cost (in millions) (in millions) (in millions)
Cost of goods sold……… $16,151.0 – $11,305.7 = $ 4,845.3
Selling, general and administrative……… 9,249.0 – 3,699.6 = 5,549.4
Total fixed cost……… $10,394.7
Number of
Total Amount Barrels Per Unit
(in millions) (in millions) Amount
Net sales……… $36,297.0 ÷ 300 = $120.99
Variable cost of goods sold……… 11,305.7 ÷ 300 = 37.69
Variable selling, general and 3,699.6 ÷ 300 = 12.33
administrative………
146,466,112 barrels
The variable costs per unit are determined by multiplying the total amount of each cost by the variable cost percentage (70% for cost of goods sold and 40% for selling, general and administrative costs), then dividing by the number of barrels. 1($16,151,000,000 × 30%) + ($9,249,000,000) × 60% 2$36,297,000,000 ÷ 300,000,000 3($16,151,000,000 × 70%) ÷ 300,000,000 4($9,249,000,000 × 40%) ÷ 300,000,000 151,397,774 barrels Ex. 19–13 (FIN MAN); Ex. 4–13 (MAN)
a. Break-Even Sales (units) =
23,000 units $125 – $105
Break-Even Sales (units) = =
Break-Even Sales (units) = = 18,400 units
$130 – $105 $460,000 b.
Fixed Costs Unit Contribution Margin
Fixed Costs Break-Even Sales (units) =
Unit Contribution Margin $460,000
b. Break-Even Sales (units) = Break-Even Sales (units) = a. Break-Even Sales (units) =
$10,394,700,000 + $350,000,000
$120.99 – $37.69 – $12.33 = Fixed Costs
Unit Contribution Margin $10,394,700,000
$120.99 – $37.69 – $12.33 =
1
3 4
$4,000 $18 – $X
$4,000 = 2,000 × ($18 – $X) $4,000
2,000 units
Ex. 19–15 (FIN MAN); Ex. 4–15 (MAN)
The cost of the promotional campaign is the fixed cost in this analysis, since we’re trying to determine the break-even adoption rate of the campaign. The contribution margin earned per new subscriber is essentially the revenue earned less the variable cost over the 12-month subscription period.
Revenue: (12 mos. – 2 free mos.) × $10/mo. = $100 per new account Variable cost: 12 mos. × $6.25/mo. = $75 per new account
Note: The variable cost is for 12 months since the costs are incurred, even during the free months.
The break-even number of subscribers necessary to cover the fixed cost of the promotion would be computed as follows:
Fixed Costs Variable cost per unit:
Variable cost per unit: Variable cost per unit:
= $2 = $18 – $X = $16 2,000 units $100 – $75 Variable cost per unit:
Unit Contribution Margin
$18 – $X
= 100,000 accounts
Contribution Margin per Unit = =
Break-Even Sales (units)
$2,500,000 Break-Even
Fixed Costs
Break-Even =
= Break-Even Sales (units)
Break-Even = 32.2 million (rounded) accounts
1Revenue per account (in millions):
$32,563 million ÷ 33.3 million = $977.9 (rounded)
2Variable cost per account (in millions, except variable cost per account):
Cost of revenue……… $17,492 × 75% = $13,119.0 Selling, general, and administrative expenses………… 9,418 × 25% = 2,354.5
Total variable cost……… $15,473.5
Divided by number of accounts……… ÷ 33.3
Variable cost per account (rounded)……… $ 464.7
3Fixed costs (in millions):
Cost of revenue……… $17,492 × 25% = $ 4,373.0 Selling, general, and administrative expenses………… 9,418 × 75% = 7,063.5 Depreciation……… 5,074 × 100% = 5,074.0
Total fixed costs……… $16,510.5
= = X =
Note to Instructors: The rate charged per minute and the number of average minutes of digital service influence the revenue per account. An interesting question is whether the costs are variable to the number of minutes or number of accounts. If we assume that the costs are variable to the number of minutes, then the break-even analysis revolves around the number of minutes. More likely, the costs are more variable to the number of accounts for this business (mostly customer acquisition and service costs), while the variable cost per minute is likely to be small.
=
$16,510.5 million X – $464.7
Revenue per Account – Variable Cost per Account
$977.9 – $464.7 33.3X $31,985.0 $960.5 (rounded) $16,510.5 million 33.3X – $15,474.5 Fixed Cost
Revenue per Account – Variable Cost per Account = 33.3 million accounts b. Break-Even = Fixed Costs a. Break-Even = $16,510.5 million Break-Even 2 3 1
a.
b. $1,500,000 (the intersection of the total sales line and the total costs line) c. The graphic format permits the user (management) to visually determine the
break-even point and the operating profit or loss for any given level of sales.
$0 $500,000 $1,000,000 $2,000,000 $2,500,000 0 4,000 8,000 12,000 16,000 20,000 Sa le s a n d Cos ts Units of Sales Break-Even Point Operating Profit Area Total Sales Line
Total Costs Operating Loss Area $600,000 $1,500,000
a. $600,000 (total fixed costs)
b. Sales (20,000 units × $125)……… $2,500,000 Fixed costs……… $ 600,000
Variable costs (20,000 units × $75)……… 1,500,000 2,100,000
Income from operations……… $ 400,000
* 20,000 units = $2,500,000 maximum sales/$125 unit selling price
c.
d. 12,000 units (the intersection of the profit line and the horizontal axis)
Ex. 19–19 (FIN MAN); Ex. 4–19 (MAN) Cost-volume-profit chart
a. break-even point d. total costs line b. operating loss area e. operating profit area c. total fixed costs f. total sales line
* ($600,000) ($500,000) ($400,000) ($300,000) ($200,000) ($100,000) $0 $100,000 $200,000 $300,000 $400,000 0 5,000 10,000 15,000 20,000
O
p
er
at
ing Pr
of
it
(
L
oss)
Units of Sales
Break-Even Point Operating Loss Area Operating Profit Area Profit Line 12,000Profit-volume chart a. break-even point b. total fixed costs c. operating loss area
d. maximum operating profit e. profit line
f. operating profit area
Ex. 19–21 (FIN MAN); Ex. 4–21 (MAN)
a. Unit Selling Price of E = ($90 × 40%) + ($105 × 60%) Unit Selling Price of E = $36 + $63 = $99
Unit Variable Cost of E = ($50 × 40%) + ($65 × 60%) Unit Variable Cost of E = $20 + $39 = $59
Unit Contribution Margin of E = $99 – $59 = $40
$620,000 $40 b. 6,200 units of baseball bats (15,500 units × 40%)
9,300 units of baseball gloves (15,500 units × 60%)
Break-Even Sales (units) = = 15,500 units Break-Even Sales (units) = Fixed Costs
a. Unit contribution margin of overall product (E):
Unit selling price of E [(20% × $1,000) + (80% × $200)]……… $360 Unit variable cost of E [(20% × $100) + (80% × $75)]……… 80 Unit contribution margin of E………$280 Fixed costs of the New York City to George Town, Grand Cayman round-trip flight:
Fuel……… $10,400
Flight crew salaries……… 4,300
Depreciation……… 10,500
Total fixed costs……… $25,200 Break-even sales (units) of overall product:
$25,200 $280 per seat
b. Business class break-even (90 seats × 20%)……… 18 seats Economy class break-even (90 seats × 80%)……… 72 seats Total break-even……… 90 seats
Ex. 19–23 (FIN MAN); Ex. 4–23 (MAN)
a. (1) Margin of Safety (dollars) = Sales – Sales at Break-Even Point Margin of Safety (dollars) = $880,000 – $660,000 = $220,000
Margin of Safety (percentage) = $220,000 ÷ $880,000 = 25% b. The break-even point (S) is determined as follows:
Break-Even Sales (dollars) = Total Fixed Costs + Total Variable Costs (at Break-Even) Break-Even Sales (dollars) = Total Fixed Costs + 60% Break-Even Sales (dollars) Break-Even Sales (dollars) = $2,325,000 + 60% Break-Even Sales (dollars)
Break-Even Sales (dollars) – 60% Break-Even Sales (dollars) = $2,325,000 40% Break-Even Sales (dollars) = $2,325,000
Break-Even Sales (dollars) = $5,812,500
If the margin of safety is 25%, the actual sales are determined as follows: Sales = Break-Even Sales (dollars) + (Sales × Margin of Safety)
Sales (dollars) = $5,812,500 + 25% Sales Sales – 25% Sales = $5,812,500
75% Sales = $5,812,500 Sales = $7,750,000 (2)
= = 90 seats (tickets)
Break-Even Sales (units)
Sales – Sales at Break-Even Point Sales
Margin of Safety (percentage) =
= Fixed Costs
Unit Contribution Margin Break-Even Sales (units)
If 420,000 units are sold and sales at the break-even point are 472,500 units, there is no margin of safety.
Ex. 19–25 (FIN MAN); Ex. 4–25 (MAN) a. Beck Inc.: $500,000 $100,000 Bryant Inc.: $750,000 $300,000
b. Beck Inc.’s income from operations would increase by 100% (5.0 × 20%), or $100,000 (100% × $100,000), and Bryant Inc.’s income from operations would increase by 50% (2.5 × 20%), or $150,000 (50% × $300,000).
c. The difference in the increases of income from operations is due to the difference in the operating leverages. Beck Inc.’s higher operating leverage means that its fixed costs are a larger percentage of contribution margin than are Bryant Inc.’s. Thus, increases in sales increase operating profit at a faster rate for Beck Inc. than for Bryant Inc.
Appendix Ex. 19–26 (FIN MAN); Appendix Ex. 4–26 (MAN) a. Variable cost of goods sold
b. Variable selling and administrative expenses c. Fixed costs
Contribution Margin Income from Operations =
=
Contribution Margin Income from Operations Operating Leverage
= 5.0
Operating Leverage = = 2.5
Operating Leverage
a.
Sales $4,440,000
Variable cost of goods sold:
Variable cost of goods manufactured $2,988,000 Less ending inventory (24,000 units × $24.90) 597,600
Variable cost of goods sold 2,390,400
Manufacturing margin $2,049,600
Variable selling and administrative expenses 115,200
Contribution margin $1,934,400
Fixed costs:
Fixed manufacturing costs $ 132,000
Fixed selling and administrative expenses 172,800 304,800
Income from operations $1,629,600
Computations:
Variable cost of goods manufactured: $3,120,000 – $132,000 = $2,988,000 Units Sold = Units Manufactured – Units in Ending Inventory
96,000 = Units Manufactured – 24,000 120,000 = Units Manufactured
Unit cost of ending inventory:
Variable cost of goods manufactured per unit: $2,988,000 ÷ 120,000 units manufactured = $24.90
Thus, variable cost of goods sold could alternatively be calculated: $2,390,400 = 96,000 units × $24.90/unit
Fixed selling and administrative expenses: $288,000 – $115,200 = $172,800
b. Absorption costing income from operations………$1,656,000 Variable costing income from operations……… 1,629,600
Difference……….……… $ 26,400
Note: The difference between the two income numbers can be reconciled as follows:
Unit change in inventory……… 24,000 units
Fixed manufacturing cost per unit……… $1.10 ($132,000 ÷ 120,000 units) Income from operations difference……… $26,400
RHYS COMPANY
Income Statement—Variable Costing For the Month Ended July 31, 2014
a.
Sales $7,450,000
Cost of goods sold:
Cost of goods manufactured (500,000 units × $14.32) $7,160,000 Less ending inventory (80,000 units × $14.32) 1,145,600
Cost of goods sold 6,014,400
Gross profit $1,435,600
Selling and administrative expenses ($80,000 + $75,000) 155,000
Income from operations $1,280,600
Computations:
Cost of goods manufactured: $7,000,000 + $160,000 = $7,160,000 Unit cost of ending inventory:
Total cost of goods manufactured:
$7,160,000 ÷ 500,000 units manufactured = $14.32
Variable costing income from operations……… $1,255,000 Absorption costing income from operations……… 1,280,600
Difference……… $ 25,600
b. Note: The difference between the two income numbers can be reconciled as follows:
Unit change in inventory……… 80,000 units
Fixed manufacturing cost per unit……… $0.32 ($160,000 ÷ 500,000 units) Income from operations difference……… $25,600
TUDOR MANUFACTURING CO. Income Statement—Absorption Costing
For the Month Ended June 30, 2014
Prob. 19–1A (FIN MAN); Prob. 4–1A (MAN)
Fixed Variable Mixed
Cost Cost Cost Cost
a. X b. X c. X d. X e. X f. X g. X h. X i. X j. X k. X l. X m. X n. X o. X p. X q. X r. X s. X t. X
1. Variable Variable Total Cost Cost Percentage Cost Cost of goods sold……… $6,200,000 × 60% = $3,720,000 Selling expenses……… 3,400,000 × 75% = 2,550,000 Administrative expenses………… 1,550,000 × 60% = 930,000
Variable Fixed
Total Cost Cost Cost
Cost of goods sold……… $6,200,000 – $3,720,000 = $2,480,000 Selling expenses……… 3,400,000 – 2,550,000 = 850,000 Administrative expenses………… 1,550,000 – 930,000 = 620,000
Total cost……… $7,200,000 $3,950,000
Total Number
Amount of Units Per Unit
Net sales……… $16,800,000 ÷ 120,000 = $140.00 Variable costs……… 7,200,000 ÷ 120,000 = 60.00 Contribution margin……… $ 9,600,000 $ 80.00 2. a. $60 ($7,200,000 ÷ 120,000 units) b. $80 ($140 – $60) $3,950,000 $80 per unit 4. Break-Even Sales (units) = Fixed Costs Unit Contribution Margin
65,000 units $3,950,000 + $1,250,000
$80 per unit
Sales (units) Fixed Costs + Target Profit Unit Contribution Margin
3. Fixed Costs
Unit Contribution Margin Break-Even
Sales (units) = = 49,375 units
5. Break-Even Sales (units) = = Break-Even Sales (units) = =
8. In favor of the proposal is the possibility of increasing income from operations from $5,650,000 to $6,000,000. However, there are many points against the proposal, including:
a. The break-even point increases by 15,625 units (from 49,375 to 65,000). b. The sales necessary to maintain the current income from operations of
$5,650,000 would be 135,625 units, or $2,187,500 (15,625 units × $140) in excess of 2014 sales.
c. If future sales remain at the 2014 level, the income from operations of $5,650,000 will decline to $4,400,000.
The company should determine the sales potential if the additional product is produced and then evaluate the advantages and the disadvantages enumerated above, in light of these sales possibilities.
$480,000 $40*
*$100 unit selling price – $60 unit variable cost
$720,000 $40 3.
1. Break-Even Sales (units) = Total Fixed Costs Unit Contribution Margin
Break-Even Sales (units) = = 12,000 units
= 18,000 units 2. Sales (units) = Fixed Costs + Target Profit
Unit Contribution Margin Sales (units) =
=
$480,000 + $240,000 $40
Total Fixed Costs
Unit Selling Price – Unit Variable Cost
= $0 $500,000 $1,000,000 $1,500,000 $2,000,000 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 20,000 S a le s and Cost s Units of Sales Sales Total Costs Operating Loss Area
Operating Profit Area
Break-Even Point
1. = 1,000 units = 30% $75,000 30% or
= 1,000 units × $250 per unit = $250,000
$250,000
Unit Selling Price – Unit Variable Cost Unit Selling Price
$250 Unit Selling Price – $175 Unit Variable Cost $250 Unit Selling Price
Contribution Margin Ratio
= Break-Even (dollars)
Break-Even (dollars) Break-Even (dollars) Contribution Margin Ratio
= =
=
Contribution Margin Ratio Total Fixed Costs
=
Unit Selling Price
= Total Fixed Costs
Unit Selling Price – Unit Variable Cost Total Fixed Costs
Unit Contribution Margin
$75,000
$250 Unit Selling Price – $175 Unit Variable Cost
= Unit Contribution Margin
= = Break-Even Units:
Break-Even Dollars:
Break-Even Sales (units)
Break-Even (units) $0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 0 500 1,000 1,500 2,000 2,500 Sal e s and C o st s Units of Sales Total Sales Total Costs Break-Even Point Operating Profit Area Operating Loss Area $250,000 $75,000
2.
Units sold: $500,000 ÷ $250 per unit = 2,000 units
a. b. 2,000 units 2,500 units Sales……… $500,000 $625,000 Variable costs……… $350,000 $437,500 Fixed costs……… 75,000 75,000 Total costs……… $425,000 $512,500 Income from operations……… $ 75,000 $112,500
$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 0 500 1,000 1,500 2,000 2,500 Sa le s an d Co s ts Units of Sales Total Sales Total Costs Operating Profit Area Break-Even Point Operating Loss Area $512,500 $425,000 $625,000 a. . b. $75,000
3. Break-Even Units: = 1,450 units Break-Even Dollars: = 30% or = = = $362,500 Unit Contribution Margin
Break-Even (units) = $75,000 + $33,750
Break-Even Sales (units) = Total Fixed Costs
= Total Fixed Costs
Unit Selling Price – Unit Variable Cost
= =
$250 – $175
Contribution Margin Ratio
Contribution Margin Ratio Unit Contribution Margin
$250 Unit Selling Price – $175 Unit Variable Cost Unit Selling Price
$250 Unit Selling Price Unit Selling Price – Unit Variable Cost
Unit Selling Price
Break-Even (dollars) $75,000 + $33,750 30%
Break-Even (dollars) = Total Fixed Costs Contribution Margin Ratio $0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 0 500 1,000 1,500 2,000 2,500 Sal e s an d Costs Units of Sales Total Sales Total Costs Operating Profit Area Operating Loss Area Break-Even Point $362,500 1,450 $108,750
4. a. b. 2,000 units 2,500 units Sales……… $500,000 $625,000 Variable costs……… $350,000 $437,500 Fixed costs……… 108,750 108,750 Total costs……… $458,750 $546,250 Income from operations……… $ 41,250 $ 78,750
$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 0 500 1,000 1,500 2,000 2,500 Sa le s a n d Co s ts Units of Sales Total Sales Total Costs a. b. Operating Profit Area Break-Even Point Operating Loss Area $546,250 $458,750 $625,000 $108,750
(Overall product is labeled E.)
1. Unit Selling Price of E [($1,600 × 40%) + ($850 × 60%)]………$1,150 Unit Variable Cost of E [($800 × 40%) + ($350 × 60%)]……… 530 Unit Contribution Margin of E……… $ 620
$2,498,600 $620 per unit 2. 4,030 units of E × 40% = 1,612 units of laptops
4,030 units of E × 60% = 2,418 units of tablet PCs
3. Unit selling price of E [($1,600 × 50%) + ($850 × 50%)]………$1,225 Unit variable cost of E [($800 × 50%) + ($350 × 50%)]……… 575 Unit contribution margin of E……… $ 650
$2,498,600 $650 3,844 units of E × 50% = 1,922 units of laptops 3,844 units of E × 50% = 1,922 units of tablet PCs
The break-even point is lower in this scenario than in part (1) because the sales mix is weighted toward the product with the higher contribution margin per unit of product.
Break-Even Sales (units)
Fixed Costs Unit Contribution Margin
= Fixed Costs
Unit Contribution Margin
3,844 units =
= =
4,030 units
Break-Even Sales (units) =
1.
Sales (21,875 × $160) $3,500,000
Cost of goods sold:
Direct materials (21,875 × $46) $1,006,250
Direct labor (21,875 × $40) 875,000
Factory overhead [$200,000 + (21,875 × $20)] 637,500
Cost of goods sold 2,518,750
Gross profit $ 981,250
Expenses:
Selling expenses:
Sales salaries and commissions
[$110,000 + (21,875 × $8)] $285,000
Advertising 40,000
Travel 12,000
Miscellaneous selling expense
[$7,600 + (21,875 × $1)] 29,475
Total selling expenses $366,475
Administrative expenses:
Office and officers’ salaries $132,000 Supplies [$10,000 + (21,875 × $4)] 97,500 Miscellaneous administrative expense
[$13,400 + (21,875 × $1)] 35,275
Total administrative expenses 264,775
Total expenses 631,250
Income from operations $ 350,000
WOLSEY INDUSTRIES INC. Estimated Income Statement For the Year Ended December 31, 2014
$875,000 $3,500,000 $525,000 $160 – $120 $525,000 25%
Break-Even Sales (dollars) = 13,125 units × $160 per unit = $2,100,000 2. Contribution Margin Ratio = Sales – Variable Costs
Sales
= =
=
3. Break-Even Sales (units) = Fixed Costs Unit Contribution Margin Contribution Margin Ratio = $3,500,000 – (21,875 × $120)
= = $2,100,000
= 25%
Break-Even Sales (units)
Break-Even Sales (dollars) = Fixed Costs
Contribution Margin Ratio 13,125 units $3,500,000
4. 5. Margin of safety: In dollars: Expected sales (21,875 × $160)……… $3,500,000 Break-even point (13,125 × $160)……… 2,100,000 Margin of safety……… $1,400,000 As a percentage of sales: $1,400,000 $3,500,000 Margin of Safety = = 40% =
Margin of Safety Sales – Sales at Break-Even Point Sales $0 $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000 $3,000,000 $3,500,000 $4,000,000 $4,500,000 0 3,000 6,000 9,000 12,000 15,000 18,000 21,000 24,000 27,000 S a le s an d C o sts Units Sales Total Costs Operating Profit Area Break-Even Point Operating Loss Area $2,100,000 13,125 $525,000
Fixed Variable Mixed
Cost Cost Cost Cost
a. X b. X c. X d. X e. X f. X g. X h. X i. X j. X k. X l. X m. X n. X o. X p. X q. X r. X s. X t. X
1. Total Variable Cost Variable
Cost Percentage Cost
Cost of goods sold……… $1,400,000 × 75% = $1,050,000
Selling expenses……… 400,000 × 60% = 240,000
Administrative expenses……… 387,500 × 80% = 310,000
Total Variable Fixed
Cost Cost Cost
Cost of goods sold……… $1,400,000 – $1,050,000 = $350,000 Selling expenses……… 400,000 – 240,000 = 160,000 Administrative expenses……… 387,500 – 310,000 = 77,500
Total cost……… $1,600,000 $587,500
Number
Total Amount of Units Per Unit Net sales……… $2,880,000 ÷ 64,000 = $45.00 Variable costs……… 1,600,000 ÷ 64,000 = 25.00 Contribution margin……… $1,280,000 $20.00 2. a. $25 ($1,600,000 ÷ 64,000 units) b. $20 ($45 – $25) $587,500 $20 per unit $1,492,500 5. Break-Even Sales (units) $800,000 + $692,500 Unit Contribution Margin 4. Break-Even
Sales (units) =
3. Fixed Costs
Unit Contribution Margin Break-Even
Sales (units) = = 29,375 units
40,000 units =
Fixed Costs + Target Profit $587,500 + $212,500 $20 per unit Sales (units) = = Break-Even Sales (units) = Fixed Costs Unit Contribution Margin
8. In favor of the proposal is the possibility of increasing income from operations from $692,500 to $880,000. However, there are many points against the
proposal, including:
a. The break-even point increases by 10,625 units (from 29,375 to 40,000). b. The sales necessary to maintain the current income from operations of
$692,500 would be 74,625 units, or $478,125 (10,625 units × $45) in excess of 2014 sales.
c. If future sales remain at the 2014 level, the income from operations of $692,500 will decline to $480,000.
The company should determine the sales potential if the additional product is produced and then evaluate the advantages and the disadvantages enumerated above, in light of these sales possibilities.
$800,000 $40*
*$150 unit selling price – $110 unit variable cost
$1,100,000 $40 per unit 3.
=
Unit Selling Price – Unit Variable Cost 1. Break-Even Sales (units) = Total Fixed Costs
Unit Contribution Margin Total Fixed Costs
$800,000 + $300,000 Sales (units) =
2. Sales (units) = Total Fixed Costs + Target Profit Unit Contribution Margin
27,500 units 20,000 units
= =
$40 per unit Break-Even Sales (units) = =
$0 $1,000,000 $2,000,000 $3,000,000 $4,000,000 $5,000,000 $6,000,000 $7,000,000 Sal es a n d Co sts Sales Total Costs Operating Loss Area Break-Even Point
Break-Even Units: = 3,000 units Break-Even Dollars: = 37.5% $225,000 37.5% or
Break-Even (dollars) = 3,000 units × $200 per unit Unit Selling Price
= $600,000
=
$200 Unit Selling Price Unit Selling Price – Unit Variable Cost
Unit Selling Price Total Fixed Costs
Break-Even (dollars) =
Break-Even (units) =
Contribution Margin Ratio =
Contribution Margin Ratio = Unit Contribution Margin
Break-Even (dollars) = Total Fixed Costs Contribution Margin Ratio
1.
$200 Unit Selling Price – $125 Unit Variable Cost $200 Unit Selling Price – $125 Unit Variable Cost
$225,000 Unit Contribution Margin
Unit Selling Price – Unit Variable Cost Break-Even Sales (units) = Total Fixed Costs
= $0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000 $1,400,000 0 1,500 3,000 4,500 6,000 7,500 S a le s a n d C o st s Units of Sales Total Sales Total Costs Break-Even Point Operating Profit Area Operating Loss Area $225,000
2. a. b. 4,500 units 7,500 units Sales……… $900,000 $1,500,000 Variable costs……… $562,500 $ 937,500 Fixed costs……… 225,000 225,000 Total costs……… $787,500 $1,162,500 Income from operations……… $112,500 $ 337,500
$0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000 $1,400,000 $1,600,000 0 1,500 3,000 4,500 6,000 7,500 S a le s an d C o st s Units of Sales Total Sales Total Costs Operating Profit Area Break-Even Point Operating Loss Area $787,500 $1,500,000 $1,162,500 $900,000 a. b. $225,000
3.
= 4,500 units
= 37.5%
or
= $900,000 Unit Contribution Margin
Unit Selling Price – Unit Variable Cost Unit Selling Price
$200 Unit Selling Price – $125 Unit Variable Cost
Unit Contribution Margin
$200 Unit Selling Price – $125 Unit Variable Cost $200 Unit Selling Price
=
Unit Selling Price = Total Fixed Costs
=
Unit Selling Price – Unit Variable Cost Total Fixed Costs
=
= $225,000 + $112,500
=
Break-Even (dollars) Contribution Margin Ratio
=
= Break-Even (dollars)
Total Fixed Costs Contribution Margin Ratio
$225,000 + $112,500 37.5%
Contribution Margin Ratio Break-Even Dollars:
Break-Even Units:
Break-Even Sales (units)
Break-Even (units) $0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000 $1,400,000 $1,600,000 0 1,500 3,000 4,500 6,000 7,500 Sal e s a n d C o s ts Units of Sales Total Sales Total Costs Operating Profit Area Operating Loss Area Break-Even Point $900,000 $337,500
4. a. b. 6,000 units 7,500 units Sales……… $1,200,000 $1,500,000 Variable costs……… $ 750,000 $ 937,500 Fixed costs……… 337,500 337,500 Total costs………$1,087,500 $1,275,000 Income from operations……… $ 112,500 $ 225,000
$0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000 $1,400,000 $1,600,000 0 1,500 3,000 4,500 6,000 7,500 Sa le s an d C o st s Units of Sales Total Sales Total Costs a. b. Operating Profit Area Break-Even Point Operating Loss Area $1,500,000 $1,275,000 $1,087,500 $337,500
(Overall product is labeled E.)
1. Unit Selling Price of E [($12 × 30%) + ($15 × 70%)]………$14.10 Unit Variable Cost of E [($3 × 30%) + ($4 × 70%)]……… 3.70 Unit Contribution Margin of E……… $10.40
$46,800 $10.40 per unit 2. 4,500 units of E × 30% = 1,350 units of 12-inch pizza
4,500 units of E × 70% = 3,150 units of 16-inch pizza
3. Unit selling price of E [($12 × 50%) + ($15 × 50%)]………$13.50 Unit variable cost of E [($3 × 50%) + ($4 × 50%)]……… 3.50 Unit contribution margin of E……… $10.00
$46,800 $10.00
4,680 units of E × 50% = 2,340 units of 12-inch pizza 4,680 units of E × 50% = 2,340 units of 16-inch pizza
The break-even point is higher in scenario 2 because the mix changes to be less weighted toward the higher contribution margin per unit product in part (3).
Break-Even Sales (units)
=
= Fixed Costs
Unit Contribution Margin
4,680 units =
=
Break-Even Sales (units) = Fixed Costs Unit Contribution Margin =
4,500 units Break-Even Sales (units)
1.
Sales (12,000 × $240) $2,880,000
Cost of goods sold:
Direct materials (12,000 × $50) $600,000
Direct labor (12,000 × $30) 360,000
Factory overhead [$350,000 + (12,000 × $6)] 422,000
Cost of goods sold 1,382,000
Gross profit $1,498,000
Expenses:
Selling expenses:
Sales salaries and commissions
[$340,000 + (12,000 × $4)] $388,000
Advertising 116,000
Travel 4,000
Miscellaneous selling expense
[$2,300 + (12,000 × $1)] 14,300
Total selling expenses $522,300
Administrative expenses:
Office and officers’ salaries $325,000 Supplies [$6,000 + (12,000 × $4)] 54,000 Miscellaneous administrative expense
[$8,700 + (12,000 × $1)] 20,700
Total administrative expenses 399,700
Total expenses 922,000
Income from operations $ 576,000
BELMAIN CO.
Estimated Income Statement For the Year Ended December 31, 2014
$1,728,000 $2,880,000 $1,152,000 $240 – $96 $1,152,000 60%
Break-Even Sales (dollars) = 8,000 units × $240 per unit = $1,920,000 3. Break-Even Sales (units) = Fixed Costs
Unit Contribution Margin 2. Contribution Margin Ratio = Sales – Variable Costs
Sales
Break-Even Sales (dollars) = Fixed Costs
Contribution Margin Ratio
= = $1,920,000
8,000 units 60%
$2,880,000
Contribution Margin Ratio = $2,880,000 – (12,000 × $96)
= =
= =
4.
5. Margin of safety: In dollars:
Expected sales (12,000 units × $240)……… $2,880,000 Break-even point (8,000 units × $240)……… 1,920,000 Margin of safety……… $ 960,000 As a percentage of sales: $960,000 $2,880,000 6. = =
Margin of Safety Sales – Sales at Break-Even Point Sales = Margin of Safety Contribution Margin 33.3% Operating Leverage = $0 $500,000 $1,000,000 $1,500,000 $2,000,000 $2,500,000 $3,000,000 $3,500,000 $4,000,000 $4,500,000 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000 Sa les a n d Co sts Units Sales Total Costs Operating Profit Area Break-Even Point Operating Loss Area $1,920,000 $1,152,000
CP 19–1 (FIN MAN); CP 4–1 (MAN)
In an absolute sense, Edward’s actions are devious. He is clearly attempting to use the first four-year scenario, which is favorable, as a way to market the partnerships. They are really longer-term investments. After the first four years, the risk increases dramatically. The break-even occupancy becomes much more difficult to achieve at 95% than it does at 65%. Focusing on the 65% and remaining silent about the increase to 95% is deceptive. One might argue “let the buyer beware.” After all, the information is in the fine print. A little spadework would reveal the longer-term reality of these partnerships. This is not a compelling argument. Clearly, Edward is putting some favorable spin on this offering. It’s likely that this will come back to haunt him in a court of law. Some investors may claim they were defrauded by less than complete disclosure. Edward has a responsibility to provide objective information. The integrity standard requires that Edward communicate constraints that would preclude the successful performance of an activity. Also, Edward must communicate unfavorable as well as favorable information. Clearly, the increase in the mortgage rate and its impact on the break-even point is unfavorable information that should be given as much visibility as the favorable 65% break-even information.
The airline industry has a high operating leverage. This means that fixed costs are a large part of the cost structure. The break-even volume is apparently around 65% of capacity. When the volume falls below 65%, the industry loses money. As the percentage increases above 65%, the industry becomes very profitable. There is a difference between profitability and cash flow. Since a large part of the cost structure in airlines is fixed costs, this means that depreciation makes up a large part of the expense base. Depreciation is a noncash expense. Therefore, it is likely that the industry is not profitable but has positive cash flow at capacity use that is below break-even. There is a point, however, where the industry will not generate sufficient cash to maintain operations.
The airline strategy of raising ticket prices and consolidating routes may be a successful strategy; however, there are a number of considerations. First, the higher ticket prices would increase the revenue per passenger-mile and reduce the break-even occupancy percentage only if it is assumed that there is no change in passenger volume. However, this is unlikely. The revenue from price increases would need to increase faster than the lost revenue from lower traffic volume for a price increase to lower break-even. To raise ticket prices, the airline would have to minimize the impact on lost volume. This might be possible for fare increases targeted to business travelers that need to fly, regardless of ticket price. The airline can minimize volume losses by keeping fares lower for nonbusiness travelers. Restrictions such as allowing reduced fares only on round-trip fares that go over a Saturday night achieve this objective, since business travelers do not wish to be out of town over the weekend. Likewise, requiring higher fares for seats reserved with little advance notice would also achieve this objective, since much business travel cannot be planned weeks in advance.
The strategy of consolidating routes attacks a major cost of airlines. The number of flights and terminals served drives fuel and airport ground- and terminal-related costs. Therefore, consolidating routes by either reducing the number of terminals served and/or the number of flights is a method of achieving some economies of scale. For example, an airline could consolidate three flights departing in the morning from Tulsa to Dallas into just two flights departing in the morning. This
Do-Nothing Strategy:
Revenue – Variable Costs – Fixed Costs = Profit ($80 × 1,000,000) – ($35 × 1,000,000) – $35,000,000 = Profit $80,000,000 – $35,000,000 – $35,000,000 = $10,000,000 Thomas’s Strategy:
Revenue – Variable Costs – Fixed Costs = Profit ($60 × 2,000,000) – ($35 × 2,000,000) – $35,000,000 = Profit $120,000,000 – $70,000,000 – $35,000,000 = $15,000,000 James’s Strategy:
Revenue – Variable Costs – Fixed Costs = Profit ($80 × 1,400,000) – ($35 × 1,400,000) – $45,000,000 = Profit $112,000,000 – $49,000,000 – $45,000,000 = $18,000,000 James’s strategy, which is to maintain the price but increase advertising,
appears superior.
CP 19–4 (FIN MAN); CP 4–4 (MAN)
The direct labor costs are not variable to the increase in unit volume. The unit volume is the wrong activity base for direct labor costs. The “number of
impressions” is a more accurate reflection of the direct labor cost. An impression is a separate printing color application on the banners. Thus, the analysis should be done as follows:
One Three
Color Color Total
Number of banners 212 616 1,800
Number of impressions 212 1,848 5,400
Last year’s impressions: 1,800 (180 + 480 + 1,140)
Thus, a 125% assumed increase from the unit volume information will understate the potential increase in direct labor cost.
Total increase: Two Color 274 548 5,400 – 1,800 1,800 = 200% Color Four 698 2,792
The Shipping Department manager should respond by pointing out that the activities performed by his department are not related to sales volume but to sales orders. The orders require inventory pulling and sorting activities as well as paperwork activities. Thus, even though the sales volume is decreasing, the number of sales orders processed has increased from 1,180 to 1,475 (25%) over the last eight months. The reason for this increase in sales orders is that
customers are ordering lower quantities per order than in the past. Thus, it is no wonder that the Shipping Department manager is experiencing financial pressure. The amount of work performed by the department is increasing, even though sales volume is down.
CP 19–6 (FIN MAN); CP 4–6 (MAN)
There are many possible applications of break-even analysis in a school environment. Below are just a few possible ideas.
Revenue Fixed Costs Variable Costs
1 Break-even number Student tuition Faculty salary, space Supplies, copying of students in a class for a class costs
2 Break-even sales Book sales Manager’s salary, Cashier salaries,
in the bookstore space costs cost of books
3 Break-even daily Meal revenue Salaries, space Food costs meal revenues
4 Break-even students Room revenue Space, staff salaries, Janitorial costs
in a dorm utilities
5 Break-even number Ticket and Space, staff Clean-up costs, of tickets sold for a concession salaries, utilities concession costs basketball game revenue
6 Break-even number Network user fees Network depreciation, User support, of users on a computer network maintenance, electricity
network trunk line lease costs
7 Break-even number Ticket revenue Concert hall Salaries of some Break-Even Analysis
